TSTP Solution File: NUM636^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM636^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 08:55:51 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 11 unt; 4 typ; 0 def)
% Number of atoms : 43 ( 42 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 145 ( 37 ~; 17 |; 2 &; 86 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 14 ^ 26 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
one: $i ).
thf(decl_23,type,
succ: $i > $i ).
thf(decl_24,type,
esk1_0: $i ).
thf(decl_25,type,
esk2_1: ( $i > $o ) > $i ).
thf(satz2,conjecture,
! [X1: $i] :
( ( succ @ X1 )
!= X1 ),
file('/export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p',satz2) ).
thf(induction,axiom,
! [X3: $i > $o] :
( ( ( X3 @ one )
& ! [X1: $i] :
( ( X3 @ X1 )
=> ( X3 @ ( succ @ X1 ) ) ) )
=> ! [X2: $i] : ( X3 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p',induction) ).
thf(one_is_first,axiom,
! [X1: $i] :
( ( succ @ X1 )
!= one ),
file('/export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p',one_is_first) ).
thf(succ_injective,axiom,
! [X1: $i,X2: $i] :
( ( ( succ @ X1 )
= ( succ @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p',succ_injective) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: $i] :
( ( succ @ X1 )
!= X1 ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz2])]) ).
thf(c_0_5,plain,
! [X15: $i > $o,X17: $i] :
( ( ( X15 @ ( esk2_1 @ X15 ) )
| ~ ( X15 @ one )
| ( X15 @ X17 ) )
& ( ~ ( X15 @ ( succ @ ( esk2_1 @ X15 ) ) )
| ~ ( X15 @ one )
| ( X15 @ X17 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[induction])])])])])]) ).
thf(c_0_6,negated_conjecture,
( ( succ @ esk1_0 )
= esk1_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
thf(c_0_7,plain,
! [X1: $i] :
( ( succ @ X1 )
!= one ),
inference(fof_simplification,[status(thm)],[one_is_first]) ).
thf(c_0_8,plain,
! [X1: $i,X3: $i > $o] :
( ( X3 @ X1 )
| ~ ( X3 @ ( succ @ ( esk2_1 @ X3 ) ) )
| ~ ( X3 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
( ( succ @ esk1_0 )
= esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X12: $i] :
( ( succ @ X12 )
!= one ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
thf(c_0_11,plain,
! [X1: $i] :
( ( X1
!= ( succ @ X1 ) )
| ( one
= ( succ @ one ) )
| ( ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
= ( succ
@ ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_8,c_0_9]) ).
thf(c_0_12,plain,
! [X1: $i] :
( ( succ @ X1 )
!= one ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,plain,
! [X1: $i,X3: $i > $o] :
( ( X3 @ ( esk2_1 @ X3 ) )
| ( X3 @ X1 )
| ~ ( X3 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_14,plain,
! [X13: $i,X14: $i] :
( ( ( succ @ X13 )
!= ( succ @ X14 ) )
| ( X13 = X14 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[succ_injective])])]) ).
thf(c_0_15,plain,
! [X1: $i] :
( ( ( succ
@ ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) )
= ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) )
| ( ( succ @ X1 )
!= X1 ) ),
inference(sr,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
! [X1: $i] :
( ( X1
!= ( succ @ X1 ) )
| ( ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) )
!= ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) )
| ( one
= ( succ @ one ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_13,c_0_9]) ).
thf(c_0_17,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( succ @ X1 )
!= ( succ @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
( ( succ
@ ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) )
= ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
thf(c_0_19,plain,
! [X1: $i] :
( ( ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
!= ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
| ( ( succ @ X1 )
!= X1 ) ),
inference(sr,[status(thm)],[c_0_16,c_0_12]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ( ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
= X1 )
| ( ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
!= ( succ @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
( ( succ
@ ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) )
!= ( esk2_1
@ ^ [Z0: $i] :
( Z0
!= ( succ @ Z0 ) ) ) ),
inference(spm,[status(thm)],[c_0_19,c_0_9]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : NUM636^2 : TPTP v8.1.2. Released v3.7.0.
% 0.08/0.10 % Command : run_E %s %d THM
% 0.09/0.29 % Computer : n025.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri May 3 09:30:13 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.14/0.39 Running higher-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p
% 0.14/0.40 # Version: 3.1.0-ho
% 0.14/0.40 # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.14/0.40 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40 # Starting new_ho_14 with 1500s (5) cores
% 0.14/0.40 # Starting full_lambda_8 with 300s (1) cores
% 0.14/0.40 # Starting new_ho_13 with 300s (1) cores
% 0.14/0.40 # Starting ho_unfolding_3 with 300s (1) cores
% 0.14/0.40 # new_ho_14 with pid 32412 completed with status 0
% 0.14/0.40 # Result found by new_ho_14
% 0.14/0.40 # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.14/0.40 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40 # Starting new_ho_14 with 1500s (5) cores
% 0.14/0.40 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.40 # Search class: HGUSF-FFSF11-DSFFFSBN
% 0.14/0.40 # partial match(1): HGUSF-FFSF11-SSFFFSBN
% 0.14/0.40 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.40 # Starting new_ho_14 with 901s (1) cores
% 0.14/0.40 # Starting new_ho_13 with 151s (1) cores
% 0.14/0.40 # Starting ho_unfolding_6 with 151s (1) cores
% 0.14/0.40 # Starting sh4l with 151s (1) cores
% 0.14/0.40 # Starting full_lambda_8 with 146s (1) cores
% 0.14/0.40 # new_ho_13 with pid 32417 completed with status 0
% 0.14/0.40 # Result found by new_ho_13
% 0.14/0.40 # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.14/0.40 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40 # Starting new_ho_14 with 1500s (5) cores
% 0.14/0.40 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.40 # Search class: HGUSF-FFSF11-DSFFFSBN
% 0.14/0.40 # partial match(1): HGUSF-FFSF11-SSFFFSBN
% 0.14/0.40 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.40 # Starting new_ho_14 with 901s (1) cores
% 0.14/0.40 # Starting new_ho_13 with 151s (1) cores
% 0.14/0.40 # Preprocessing time : 0.001 s
% 0.14/0.40 # Presaturation interreduction done
% 0.14/0.40
% 0.14/0.40 # Proof found!
% 0.14/0.40 # SZS status Theorem
% 0.14/0.40 # SZS output start CNFRefutation
% See solution above
% 0.14/0.40 # Parsed axioms : 6
% 0.14/0.40 # Removed by relevancy pruning/SinE : 2
% 0.14/0.40 # Initial clauses : 5
% 0.14/0.40 # Removed in clause preprocessing : 0
% 0.14/0.40 # Initial clauses in saturation : 9
% 0.14/0.40 # Processed clauses : 25
% 0.14/0.40 # ...of these trivial : 0
% 0.14/0.40 # ...subsumed : 2
% 0.14/0.40 # ...remaining for further processing : 23
% 0.14/0.40 # Other redundant clauses eliminated : 0
% 0.14/0.40 # Clauses deleted for lack of memory : 0
% 0.14/0.40 # Backward-subsumed : 2
% 0.14/0.40 # Backward-rewritten : 1
% 0.14/0.40 # Generated clauses : 12
% 0.14/0.40 # ...of the previous two non-redundant : 9
% 0.14/0.40 # ...aggressively subsumed : 0
% 0.14/0.40 # Contextual simplify-reflections : 0
% 0.14/0.40 # Paramodulations : 10
% 0.14/0.40 # Factorizations : 0
% 0.14/0.40 # NegExts : 0
% 0.14/0.40 # Equation resolutions : 2
% 0.14/0.40 # Disequality decompositions : 0
% 0.14/0.40 # Total rewrite steps : 1
% 0.14/0.40 # ...of those cached : 0
% 0.14/0.40 # Propositional unsat checks : 0
% 0.14/0.40 # Propositional check models : 0
% 0.14/0.40 # Propositional check unsatisfiable : 0
% 0.14/0.40 # Propositional clauses : 0
% 0.14/0.40 # Propositional clauses after purity: 0
% 0.14/0.40 # Propositional unsat core size : 0
% 0.14/0.40 # Propositional preprocessing time : 0.000
% 0.14/0.40 # Propositional encoding time : 0.000
% 0.14/0.40 # Propositional solver time : 0.000
% 0.14/0.40 # Success case prop preproc time : 0.000
% 0.14/0.40 # Success case prop encoding time : 0.000
% 0.14/0.40 # Success case prop solver time : 0.000
% 0.14/0.40 # Current number of processed clauses : 11
% 0.14/0.40 # Positive orientable unit clauses : 2
% 0.14/0.40 # Positive unorientable unit clauses: 0
% 0.14/0.40 # Negative unit clauses : 4
% 0.14/0.40 # Non-unit-clauses : 5
% 0.14/0.40 # Current number of unprocessed clauses: 2
% 0.14/0.40 # ...number of literals in the above : 4
% 0.14/0.40 # Current number of archived formulas : 0
% 0.14/0.40 # Current number of archived clauses : 13
% 0.14/0.40 # Clause-clause subsumption calls (NU) : 14
% 0.14/0.40 # Rec. Clause-clause subsumption calls : 14
% 0.14/0.40 # Non-unit clause-clause subsumptions : 1
% 0.14/0.40 # Unit Clause-clause subsumption calls : 4
% 0.14/0.40 # Rewrite failures with RHS unbound : 0
% 0.14/0.40 # BW rewrite match attempts : 1
% 0.14/0.40 # BW rewrite match successes : 1
% 0.14/0.40 # Condensation attempts : 0
% 0.14/0.40 # Condensation successes : 0
% 0.14/0.40 # Termbank termtop insertions : 959
% 0.14/0.40 # Search garbage collected termcells : 116
% 0.14/0.40
% 0.14/0.40 # -------------------------------------------------
% 0.14/0.40 # User time : 0.004 s
% 0.14/0.40 # System time : 0.001 s
% 0.14/0.40 # Total time : 0.005 s
% 0.14/0.40 # Maximum resident set size: 1860 pages
% 0.14/0.40
% 0.14/0.40 # -------------------------------------------------
% 0.14/0.40 # User time : 0.011 s
% 0.14/0.40 # System time : 0.007 s
% 0.14/0.40 # Total time : 0.018 s
% 0.14/0.40 # Maximum resident set size: 1708 pages
% 0.14/0.40 % E---3.1 exiting
% 0.14/0.40 % E exiting
%------------------------------------------------------------------------------